Elizabeth Greene/Green -born 1821

I have been searching for some time for anything on the parents of my ggGrandmother, Elizabeth Green(e) Hannon, who was born in 1821. The family records say she was born in TN, but it could have been in Rutherford Co., NC. She married my ggGrandfather Thomas Warren Hannon in 1842 in NC.
They are in the 1850 census in NC. Thomas died in 1882 in Kansas, Elizabeth about 1885, also in Kansas.
I found an H.B. Green, also in Rutherford in 1850, living near Elizabeth and Thomas Hannon. I believe this may have been a brother of Elizabeth, but can't verify.
Can anyone help me with the parents of Elizabeth? It will be greatly appreciated.
Thanks
Kathy